Fidelity_Project
Weiling Li
10/17/2019
Sector Fund
For this project sector fund Fidelity Select Technology Portfolio (FSPTX) is chosen as the target fund. On Fidelity’s website, this is categorized as: Large Growth
For comparison, Russel2000(^RUT), NASDAQ(^IXIC), S&P500(^GSPC), S&PMidCap(^MID) and S&PSmlCap(^SML) was selected as initial indexes to be campared with.
for comparison, Vanguard’s similar index funds are also loaded as IT ETF(VGT),LargeCap ETF(VIGAX) and TotalMarket ETF(VTSAX)
Before loading data, we will define some useful function to ease the data cleaning process, and claim some variables 1st.
## this function requires a dataframe input that has the daily close price named:Closed and a date column named: Date with format as: floating point and "xxxx(year)-xx(month)-xx(day)"
## We trimmed the data from 1990-10-07 because 1990-10-08 is a Monday and Stock market closed during weekend
dailynlogReturn <- function(Date1,DataFrame){
DataFrame = mutate(DataFrame, dailyReturn = (Close-lag(Close))/Close)%>%mutate(perc_dailyRe = round(dailyReturn*100.0,3))%>%mutate(log.Close = log(Close))%>%filter(Date >= Date1)%>%filter(Date <= as.Date("2018-12-31"))
}
## This function returns a projection value of the fund from the start date and assuming 10k investment from the start and reinvest all earnings
getProjectionValue <- function(DF){
P0 = pull(filter(DF, Date == pull(top_n(DF["Date"],-1)))%>%select(Close))
DF = mutate(DF,ProjValper10k = (Close*10000)/P0)
}
## Calculate Euclidean distances between two sets of data
sqerr <- function(x,y){
z = x - y
z = sqrt(dot(z,z)/length(y))
return(z)
}
## function for standarize NAV
standardizedNAV = function(DF){
return(mutate(DF,Close.z = (Close-mean(Close))/sd(Close)))
}
## restrict ourselves to study data after 2014-01-01
StartDate = as.Date("2014-01-01")Load and clean the data, then some EDA
Load the data:
FSPTX = dailynlogReturn(StartDate,read_csv("FSPTX.csv"))
NASDAQ = dailynlogReturn(StartDate,read_csv("^IXIC.csv"))
SnP500 = dailynlogReturn(StartDate,read_csv("^GSPC.csv"))
SnPMID = dailynlogReturn(StartDate,read_csv("^MID.csv"))
SnPSML = dailynlogReturn(StartDate,read_csv("^SML.csv"))
RUSSELL2000 = dailynlogReturn(StartDate,read_csv("^RUT.csv"))
VGT = dailynlogReturn(StartDate,read_csv("VGT.csv"))
VIGAX = dailynlogReturn(StartDate,read_csv("VIGAX.csv"))
VTSAX = dailynlogReturn(StartDate,read_csv("VTSAX.csv"))Standardize NAV
FSPTX = standardizedNAV(FSPTX)
NASDAQ = standardizedNAV(NASDAQ)
SnP500 = standardizedNAV(SnP500)
SnPMID = standardizedNAV(SnPMID)
SnPSML = standardizedNAV(SnPSML)
RUSSELL2000 = standardizedNAV(RUSSELL2000)
VGT = standardizedNAV(VGT)
VIGAX = standardizedNAV(VIGAX)
VTSAX = standardizedNAV(VTSAX)Plot the NAVs:
plotly_build(ggplot(FSPTX)+ theme(legend.position="top")+geom_line(mapping = aes(x = Date,y = Close.z,color = "FSPTX"))+geom_line(mapping = aes(x = NASDAQ$Date,y = NASDAQ$Close.z,color = "NASDAQ"),alpha = .4)+geom_line(mapping = aes(x = SnP500$Date,y = SnP500$Close.z,color = "S&P 500"),alpha = .4)+geom_line(mapping = aes(x = SnPMID$Date,y = SnPMID$Close.z,color = "S&PmidCAP"),alpha = .4)+geom_line(mapping = aes(x = SnPSML$Date,y = SnPSML$Close.z,color = "S&PsmlCAP"),alpha = .4)+geom_line(mapping = aes(x = RUSSELL2000$Date,y = RUSSELL2000$Close.z,color = "Russell2000"),alpha = .4)+geom_line(mapping = aes(x = VGT$Date,y = VGT$Close.z,color = "IT ETF"),alpha = .4)+geom_line(mapping = aes(x = VTSAX$Date,y = VTSAX$Close.z,color = "TotalMarket ETF"),alpha = .4)+geom_line(mapping = aes(x = VIGAX$Date,y = VIGAX$Close.z,color = "LargeCap ETF"),alpha = .4)+ylab("standardized NAV"))%>%
layout(legend = list(orientation = 'h',x = 0.1, y = 1.4))#ggplot(VGT)+geom_line(mapping = aes(x = Date,y = Close.z,color = "VGT"))+geom_line(mapping = aes(x = NASDAQ$Date,y = NASDAQ$Close.z,color = "NASDAQ"),alpha = .4)+geom_line(mapping = aes(x = SnPMID$Date,y = SnPMID$Close.z,color = "S&PmidCAP"),alpha = .4)+geom_line(mapping = aes(x = SnPSML$Date,y = SnPSML$Close.z,color = "S&PsmlCAP"),alpha = .4)+geom_line(mapping = aes(x = RUSSELL2000$Date,y = RUSSELL2000$Close.z,color = "Russell2000"),alpha = .4)+ylab("standardized NAV")+ theme(legend.position="top")
#ggplot(VIGAX)+geom_line(mapping = aes(x = Date,y = Close.z,color = "VIGAX"))+geom_line(mapping = aes(x = NASDAQ$Date,y = NASDAQ$Close.z,color = "NASDAQ"),alpha = .4)+geom_line(mapping = aes(x = SnPMID$Date,y = SnPMID$Close.z,color = "S&PmidCAP"),alpha = .4)+geom_line(mapping = aes(x = SnPSML$Date,y = SnPSML$Close.z,color = "S&PsmlCAP"),alpha = .4)+geom_line(mapping = aes(x = RUSSELL2000$Date,y = RUSSELL2000$Close.z,color = "Russell2000"),alpha = .4)+ylab("standardized NAV")+ theme(legend.position="top")
#ggplot(VTSAX)+geom_line(mapping = aes(x = Date,y = Close.z,color = "VTSAX"))+geom_line(mapping = aes(x = NASDAQ$Date,y = NASDAQ$Close.z,color = "NASDAQ"),alpha = .4)+geom_line(mapping = aes(x = SnPMID$Date,y = SnPMID$Close.z,color = "S&PmidCAP"),alpha = .4)+geom_line(mapping = aes(x = SnPSML$Date,y = SnPSML$Close.z,color = "S&PsmlCAP"),alpha = .4)+geom_line(mapping = aes(x = RUSSELL2000$Date,y = RUSSELL2000$Close.z,color = "Russell2000"),alpha = .4)+ylab("standardized NAV")+ theme(legend.position="top")It seems that the Vanguard’s ETF’s are more correlated to the indexes. Another way to look at this is the correlation matrix:
cordat = cbind(FSPTX$Close.z,NASDAQ$Close.z,SnP500$Close.z,RUSSELL2000$Close.z,SnPMID$Close.z,SnPSML$Close.z,VGT$Close.z,VIGAX$Close.z,VTSAX$Close.z)
DailyReturncor = cbind(FSPTX$dailyReturn,NASDAQ$dailyReturn,SnP500$dailyReturn,RUSSELL2000$dailyReturn,SnPMID$dailyReturn,SnPSML$dailyReturn,VGT$dailyReturn,VIGAX$dailyReturn,VTSAX$dailyReturn)
colnames(DailyReturncor) = c("FSPTX","NASDAQ","SnP500","RUSSELL2000","SnPMID","SnPSML","VGT(IT ETF)","VIGAX(LargeCAP)","VTSAX(TotalMarket)")
DailyReturncor = data.frame(DailyReturncor)
colnames(cordat) = c("FSPTX","NASDAQ","SnP500","RUSSELL2000","SnPMID","SnPSML","VGT(IT ETF)","VIGAX(LargeCAP)","VTSAX(TotalMarket)")
cordat = data.frame(cordat)
print("Nav Correlation")## [1] "Nav Correlation"cor(cordat,cordat)## FSPTX NASDAQ SnP500 RUSSELL2000 SnPMID
## FSPTX 1.0000000 0.9332307 0.9352564 0.9390869 0.9410625
## NASDAQ 0.9332307 1.0000000 0.9939862 0.9643265 0.9775877
## SnP500 0.9352564 0.9939862 1.0000000 0.9657109 0.9863761
## RUSSELL2000 0.9390869 0.9643265 0.9657109 1.0000000 0.9854988
## SnPMID 0.9410625 0.9775877 0.9863761 0.9854988 1.0000000
## SnPSML 0.9290002 0.9795196 0.9805100 0.9898554 0.9908919
## VGT.IT.ETF. 0.9284701 0.9964530 0.9911940 0.9564776 0.9684751
## VIGAX.LargeCAP. 0.9295225 0.9979172 0.9951918 0.9612092 0.9762120
## VTSAX.TotalMarket. 0.9389925 0.9937535 0.9990944 0.9749236 0.9900590
## SnPSML VGT.IT.ETF. VIGAX.LargeCAP.
## FSPTX 0.9290002 0.9284701 0.9295225
## NASDAQ 0.9795196 0.9964530 0.9979172
## SnP500 0.9805100 0.9911940 0.9951918
## RUSSELL2000 0.9898554 0.9564776 0.9612092
## SnPMID 0.9908919 0.9684751 0.9762120
## SnPSML 1.0000000 0.9753852 0.9751635
## VGT.IT.ETF. 0.9753852 1.0000000 0.9949407
## VIGAX.LargeCAP. 0.9751635 0.9949407 1.0000000
## VTSAX.TotalMarket. 0.9851894 0.9902647 0.9948887
## VTSAX.TotalMarket.
## FSPTX 0.9389925
## NASDAQ 0.9937535
## SnP500 0.9990944
## RUSSELL2000 0.9749236
## SnPMID 0.9900590
## SnPSML 0.9851894
## VGT.IT.ETF. 0.9902647
## VIGAX.LargeCAP. 0.9948887
## VTSAX.TotalMarket. 1.0000000print("DailyReturn Correlation")## [1] "DailyReturn Correlation"cor(DailyReturncor,DailyReturncor)## FSPTX NASDAQ SnP500 RUSSELL2000 SnPMID
## FSPTX 1.0000000 0.8524479 0.7843339 0.7153186 0.7306013
## NASDAQ 0.8524479 1.0000000 0.9441383 0.8768143 0.8875944
## SnP500 0.7843339 0.9441383 1.0000000 0.8632354 0.9265818
## RUSSELL2000 0.7153186 0.8768143 0.8632354 1.0000000 0.9550725
## SnPMID 0.7306013 0.8875944 0.9265818 0.9550725 1.0000000
## SnPSML 0.6868166 0.8448600 0.8512280 0.9881849 0.9516648
## VGT.IT.ETF. 0.8573442 0.9696383 0.9137894 0.8067986 0.8322866
## VIGAX.LargeCAP. 0.8349417 0.9801079 0.9728287 0.8542041 0.8977086
## VTSAX.TotalMarket. 0.7875698 0.9490009 0.9939580 0.8968889 0.9483280
## SnPSML VGT.IT.ETF. VIGAX.LargeCAP.
## FSPTX 0.6868166 0.8573442 0.8349417
## NASDAQ 0.8448600 0.9696383 0.9801079
## SnP500 0.8512280 0.9137894 0.9728287
## RUSSELL2000 0.9881849 0.8067986 0.8542041
## SnPMID 0.9516648 0.8322866 0.8977086
## SnPSML 1.0000000 0.7818024 0.8287632
## VGT.IT.ETF. 0.7818024 1.0000000 0.9533153
## VIGAX.LargeCAP. 0.8287632 0.9533153 1.0000000
## VTSAX.TotalMarket. 0.8839901 0.9113537 0.9730942
## VTSAX.TotalMarket.
## FSPTX 0.7875698
## NASDAQ 0.9490009
## SnP500 0.9939580
## RUSSELL2000 0.8968889
## SnPMID 0.9483280
## SnPSML 0.8839901
## VGT.IT.ETF. 0.9113537
## VIGAX.LargeCAP. 0.9730942
## VTSAX.TotalMarket. 1.0000000Also we can check the corrplot of the cor matrix.
colmat <- colorRampPalette(c("red", "white", "blue"))
corrplot(cor(cordat,cordat),cl.lim = c(0.9,1.0),is.corr = FALSE,col = colmat(200),title = "NAV cor",type = "lower",tl.cex = .8,mar=c(1,1,2,1))
corrplot(cor(DailyReturncor,DailyReturncor),cl.lim = c(0.6,1.0),is.corr = FALSE,col = colmat(100),title = "DailyReturn cor",type = "lower",tl.cex = .8,mar=c(1,1,2,1))
It seems that the Fidelity fund is not really matching the indexes we chose.
Check the dailyreturn and project value
FSPTX = getProjectionValue(FSPTX)
NASDAQ = getProjectionValue(NASDAQ)
SnP500 = getProjectionValue(SnP500)
VGT = getProjectionValue(VGT)
VIGAX = getProjectionValue(VIGAX)
VTSAX = getProjectionValue(VTSAX)
SnPMID = getProjectionValue(SnPMID)
SnPSML = getProjectionValue(SnPSML)
RUSSELL2000 = getProjectionValue(RUSSELL2000)Plot them:
ggplot()+geom_line(mapping = aes(x = FSPTX$Date,y = FSPTX$ProjValper10k,color = 'FSPTX'))+geom_line(mapping = aes(x = NASDAQ$Date,y = NASDAQ$ProjValper10k,color = 'NASDAQ'),size = 1.5,alpha = .6)+geom_line(mapping = aes(x = SnP500$Date,y = SnP500$ProjValper10k,color = 'S&P500'),size = 1.5,alpha = .6)+geom_line(mapping = aes(x = VGT$Date,y = VGT$ProjValper10k,color = 'VGT(ITsecETF)'),size = 1,alpha = .2)+geom_line(mapping = aes(x = VIGAX$Date,y = VIGAX$ProjValper10k,color = 'VIGAX(LARGECAPGROWTH)'),size = 1,alpha = .2)+geom_line(mapping = aes(x = VTSAX$Date,y = VTSAX$ProjValper10k,color = 'VTSAX(TOTALSTOCK)'),size = 1,alpha = .2)+geom_line(mapping = aes(x = SnPMID$Date,y = SnPMID$ProjValper10k,color = 'S&PmidCAP'),size = 1,alpha = .2)+geom_line(mapping = aes(x = SnPSML$Date,y = SnPSML$ProjValper10k,color = 'S&PsmlCAP'),size = 1,alpha = .2)+xlab("Date")+ylab("HypoGrowth of 10,000")+ theme(legend.position="top")
Still not a good fit…
Below is just some misc works: Mainly exploring the daily return
## Check distance between projected returns
print("pointwise variance between taget fund and NASDAQ")## [1] "pointwise variance between taget fund and NASDAQ"print(sqerr(FSPTX$ProjValper10k,NASDAQ$ProjValper10k))## [1] 2189.376#ks.test()
print("pointwise variance between taget fund and S&P500")## [1] "pointwise variance between taget fund and S&P500"print(sqerr(FSPTX$ProjValper10k,SnP500$ProjValper10k))## [1] 1198.561print("pointwise variance between taget fund and IT sector ETF")## [1] "pointwise variance between taget fund and IT sector ETF"print(sqerr(FSPTX$ProjValper10k,VGT$ProjValper10k))## [1] 3437.128print("pointwise variance between taget fund and Large cap growth index fund")## [1] "pointwise variance between taget fund and Large cap growth index fund"print(sqerr(FSPTX$ProjValper10k,VIGAX$ProjValper10k))## [1] 1489.18print("pointwise variance between taget fund and Total Stock market index fund")## [1] "pointwise variance between taget fund and Total Stock market index fund"print(sqerr(FSPTX$ProjValper10k,VTSAX$ProjValper10k))## [1] 1139.656#ggplot(FSPTX)+aes(x = Date , y=perc_dailyRe) + geom_line()
## Compare daily returns
dailyReturnComp = cbind(as.Date(FSPTX$Date),FSPTX$dailyReturn,NASDAQ$dailyReturn,SnP500$dailyReturn,VGT$dailyReturn,VIGAX$dailyReturn,VTSAX$dailyReturn)
colnames(dailyReturnComp) = c("Date","FSPTX","NASDAQ","SnP500","VGT","VIGAX","VTSAX")
epsilon = 0.000000000000000001
dailyReturnComp = data.frame(dailyReturnComp)%>%mutate(Date = as_date(Date),vsNASDAQ = ifelse(NASDAQ*NASDAQ<=epsilon,FSPTX,FSPTX/NASDAQ),vsSnP500 = ifelse(SnP500*SnP500<=epsilon,FSPTX,FSPTX/SnP500),vsVGT = ifelse(VGT*VGT<=epsilon,FSPTX,FSPTX/VGT),vsVIGAX = ifelse(VIGAX*VIGAX<=epsilon,FSPTX,FSPTX/VIGAX),vsVTSAX = ifelse(VTSAX*VTSAX<=epsilon,FSPTX,FSPTX/VTSAX))%>%mutate(minusNASDAQ = FSPTX-NASDAQ,minusSnP500 = FSPTX-SnP500,minusVGT = FSPTX-VGT,minusVIGAX= FSPTX-VIGAX,minusVTSAX = FSPTX-VTSAX)
print("Average ratio of dailyReturn(FSPTX/NASDAQ")## [1] "Average ratio of dailyReturn(FSPTX/NASDAQ"print(sum(sqrt(dailyReturnComp$vsNASDAQ*dailyReturnComp$vsNASDAQ)/length(dailyReturnComp$vsNASDAQ)))## [1] 2.707788print("Average ratio of dailyReturn(FSPTX/S&P500")## [1] "Average ratio of dailyReturn(FSPTX/S&P500"print(sum(sqrt(dailyReturnComp$vsSnP500*dailyReturnComp$vsSnP500)/length(dailyReturnComp$vsSnP500)))## [1] 5.321327print("Average ratio of dailyReturn(FSPTX/VGT")## [1] "Average ratio of dailyReturn(FSPTX/VGT"print(sum(sqrt(dailyReturnComp$vsVGT*dailyReturnComp$vsVGT)/length(dailyReturnComp$vsVGT)))## [1] 2.014087print("Average ratio of dailyReturn(FSPTX/VIGAX")## [1] "Average ratio of dailyReturn(FSPTX/VIGAX"print(sum(sqrt(dailyReturnComp$vsVIGAX*dailyReturnComp$vsVIGAX)/length(dailyReturnComp$vsVIGAX)))## [1] 2.495098print("Average ratio of dailyReturn(FSPTX/NASDAQ")## [1] "Average ratio of dailyReturn(FSPTX/NASDAQ"print(sum(sqrt(dailyReturnComp$vsVTSAX*dailyReturnComp$vsVTSAX)/length(dailyReturnComp$vsVTSAX)))## [1] 3.13541dailyReturnSTD = select(dailyReturnComp,contains("minus"))%>%summarise_all(funs(sd))## Warning: funs() is soft deprecated as of dplyr 0.8.0
## Please use a list of either functions or lambdas:
##
## # Simple named list:
## list(mean = mean, median = median)
##
## # Auto named with `tibble::lst()`:
## tibble::lst(mean, median)
##
## # Using lambdas
## list(~ mean(., trim = .2), ~ median(., na.rm = TRUE))
## This warning is displayed once per session.plotly_build(ggplot(dailyReturnComp)+aes(x = Date,y = minusNASDAQ)+geom_point(alpha = .1)+geom_smooth(method = "loess",se = TRUE))ggplot(dailyReturnComp)+aes(x = Date,y = minusSnP500)+geom_point(alpha = .1)+geom_smooth(method = "loess",se = TRUE)
ggplot(dailyReturnComp)+aes(x = Date,y = minusVGT)+geom_point(alpha = .1)+geom_smooth(method = "loess",se = TRUE)
ggplot(dailyReturnComp)+aes(x = Date,y = minusVIGAX)+geom_point(alpha = .1)+geom_smooth(method = "loess",se = TRUE)
ggplot(dailyReturnComp)+aes(x = Date,y = minusVTSAX)+geom_point(alpha = .1)+geom_smooth(method = "loess",se = TRUE)
ggplot(dailyReturnComp)+aes(x = FSPTX,y = NASDAQ)+geom_point()+xlim(c(-0.15,0.15))+ylim(c(-0.15,0.15))+geom_abline(intercept = 0.0,slope = 1.0)
ggplot(dailyReturnComp)+aes(x = FSPTX,y = SnP500)+geom_point()+xlim(c(-0.15,0.15))+ylim(c(-0.15,0.15))+geom_abline(intercept = 0.0,slope = 1.0)
ggplot(dailyReturnComp)+aes(x = FSPTX,y = VGT)+geom_point()+xlim(c(-0.15,0.15))+ylim(c(-0.15,0.15))+geom_abline(intercept = 0.0,slope = 1.0)
ggplot(dailyReturnComp)+aes(x = FSPTX,y = VIGAX)+geom_point()+xlim(c(-0.15,0.15))+ylim(c(-0.15,0.15))+geom_abline(intercept = 0.0,slope = 1.0)
ggplot(dailyReturnComp)+aes(x = FSPTX,y = VTSAX)+geom_point()+xlim(c(-0.15,0.15))+ylim(c(-0.15,0.15))+geom_abline(intercept = 0.0,slope = 1.0)